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Master Thesis Report Literature Review The adiabatic turbine and compressor efficiency can be expressed as follows: ηturb=h4−h5 =T4−T5 h4 −h5s T4 −T5s ηcomp = h3s −h0 = T3s −T0 h3 − h0 T3 − T0 Using equation 2.29 and 2.30, T5 and T3 can be derived respectively as follows: (2.29) (2.30) (2.31) (2.32) (2.33) T4 −T5 =ηturbT4(1− )=ηturbT4(1−( )=T4 −ηturbT4(1−( ) k ) turb T5s T4 k−1 ) k T5s T4 k−1 T5 =T4 −ηturbT4(1− T−T T0(T3s−1) T(()k −1) ) T3−T0= 3s ηcomp k−1 comp 0= T3=T0+ 3s 0=T0+ T0 ηcomp ηcomp = 0 =T0+ 0 comp turb T −T ηcomp T0(T3s−1) T0 k−1 −1) Substituting expressions for T5 and T3 into equation 2.28 and using the following assumption for the ηcomp T(()k isentropic pressure ratio and temperature ratio. 1 ( )comp = () = turb T0 As such, the thermal efficiency of a non ideal brayton cycle can be expressed as follows: − T0 (2.35) (2.36) ηcomp (2.34) τ =T3s =())k−1 sk k−1 T4 − ηturbT4(1 − () k turb th k−1 η =1− By having a common denominator for all the terms in equation 2.37 and then perform the following (2.37) T−T(1+ 1 (()k 4 0 ηcomp comp −1)) operation: • Multiply the equation by ηcomp on both the numerator and denominator terms T0 • Factorise the numerator term and denominator term by (1 − 1 ) and ηcomp respectively τs Then the thermal efficiency of the non ideal brayton cycle can be re-expressed as follows: (1 − 1 )(T4 ηturbηcomp − τs) ηth = τs T0 (2.38) The influence of BLI on cycle performance is expressed directly via a reduction in the adiabatic compressor efficiency, ηc with the following relation: (ηcomp)BLI = ηBLI ∗ ηcomp (2.39) With ηcomp(T4 −1)−τs +1 T0 12PDF Image | Aerodynamic Design of the NASA Rotor 67 for Non Uniform Inflow
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